TSTP Solution File: SEU611^2 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : SEU611^2 : TPTP v8.2.0. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n004.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Tue May 21 03:28:33 EDT 2024

% Result   : Theorem 0.20s 0.50s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   16
% Syntax   : Number of formulae    :   39 (  10 unt;  11 typ;   0 def)
%            Number of atoms       :   91 (   4 equ;   0 cnn)
%            Maximal formula atoms :   14 (   3 avg)
%            Number of connectives :  323 (  36   ~;  31   |;   6   &; 217   @)
%                                         (   5 <=>;  28  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   21 (   7 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   19 (  19   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   13 (  11 usr;   8 con; 0-2 aty)
%            Number of variables   :   78 (  14   ^  64   !;   0   ?;  78   :)

% Comments : 
%------------------------------------------------------------------------------
thf(decl_22,type,
    in: $i > $i > $o ).

thf(decl_23,type,
    dsetconstr: $i > ( $i > $o ) > $i ).

thf(decl_24,type,
    dsetconstrEL: $o ).

thf(decl_25,type,
    dsetconstrER: $o ).

thf(decl_26,type,
    binunion: $i > $i > $i ).

thf(decl_27,type,
    binunionE: $o ).

thf(decl_28,type,
    symdiff: $i > $i > $i ).

thf(decl_29,type,
    esk1_0: $i ).

thf(decl_30,type,
    esk2_0: $i ).

thf(decl_31,type,
    esk3_0: $i ).

thf(decl_32,type,
    epred1_0: $o ).

thf(dsetconstrEL,axiom,
    ( dsetconstrEL
  <=> ! [X1: $i,X2: $i > $o,X3: $i] :
        ( ( in @ X3
          @ ( dsetconstr @ X1
            @ ^ [X4: $i] : ( X2 @ X4 ) ) )
       => ( in @ X3 @ X1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dsetconstrEL) ).

thf(dsetconstrER,axiom,
    ( dsetconstrER
  <=> ! [X1: $i,X2: $i > $o,X3: $i] :
        ( ( in @ X3
          @ ( dsetconstr @ X1
            @ ^ [X4: $i] : ( X2 @ X4 ) ) )
       => ( X2 @ X3 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dsetconstrER) ).

thf(symdiffE,conjecture,
    ( dsetconstrEL
   => ( dsetconstrER
     => ( binunionE
       => ! [X1: $i,X5: $i,X3: $i] :
            ( ( in @ X3 @ ( symdiff @ X1 @ X5 ) )
           => ! [X6: $o] :
                ( ( ( in @ X3 @ X1 )
                 => ( ~ ( in @ X3 @ X5 )
                   => X6 ) )
               => ( ( ~ ( in @ X3 @ X1 )
                   => ( ( in @ X3 @ X5 )
                     => X6 ) )
                 => X6 ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',symdiffE) ).

thf(binunionE,axiom,
    ( binunionE
  <=> ! [X1: $i,X5: $i,X3: $i] :
        ( ( in @ X3 @ ( binunion @ X1 @ X5 ) )
       => ( ( in @ X3 @ X1 )
          | ( in @ X3 @ X5 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionE) ).

thf(symdiff,axiom,
    ( symdiff
    = ( ^ [X1: $i,X5: $i] :
          ( dsetconstr @ ( binunion @ X1 @ X5 )
          @ ^ [X3: $i] :
              ( ~ ( in @ X3 @ X1 )
              | ~ ( in @ X3 @ X5 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',symdiff) ).

thf(c_0_5,plain,
    ( dsetconstrEL
  <=> ! [X1: $i,X2: $i > $o,X3: $i] :
        ( ( in @ X3
          @ ( dsetconstr @ X1
            @ ^ [Z0: $i] : ( X2 @ Z0 ) ) )
       => ( in @ X3 @ X1 ) ) ),
    inference(fof_simplification,[status(thm)],[dsetconstrEL]) ).

thf(c_0_6,plain,
    ( dsetconstrER
  <=> ! [X1: $i,X2: $i > $o,X3: $i] :
        ( ( in @ X3
          @ ( dsetconstr @ X1
            @ ^ [Z0: $i] : ( X2 @ Z0 ) ) )
       => ( X2 @ X3 ) ) ),
    inference(fof_simplification,[status(thm)],[dsetconstrER]) ).

thf(c_0_7,negated_conjecture,
    ~ ( ! [X20: $i,X21: $i > $o,X22: $i] :
          ( ( in @ X22 @ ( dsetconstr @ X20 @ X21 ) )
         => ( in @ X22 @ X20 ) )
     => ( ! [X23: $i,X24: $i > $o,X25: $i] :
            ( ( in @ X25 @ ( dsetconstr @ X23 @ X24 ) )
           => ( X24 @ X25 ) )
       => ( ! [X26: $i,X27: $i,X28: $i] :
              ( ( in @ X28 @ ( binunion @ X26 @ X27 ) )
             => ( ( in @ X28 @ X26 )
                | ( in @ X28 @ X27 ) ) )
         => ! [X1: $i,X5: $i,X3: $i] :
              ( ( in @ X3 @ ( symdiff @ X1 @ X5 ) )
             => ! [X6: $o] :
                  ( ( ( in @ X3 @ X1 )
                   => ( ~ ( in @ X3 @ X5 )
                     => X6 ) )
                 => ( ( ~ ( in @ X3 @ X1 )
                     => ( ( in @ X3 @ X5 )
                       => X6 ) )
                   => X6 ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(assume_negation,[status(cth)],[symdiffE]),binunionE]),c_0_5]),c_0_6])])]) ).

thf(c_0_8,plain,
    ( symdiff
    = ( ^ [Z0: $i,Z1: $i] :
          ( dsetconstr @ ( binunion @ Z0 @ Z1 )
          @ ^ [Z2: $i] :
              ( ~ ( in @ Z2 @ Z0 )
              | ~ ( in @ Z2 @ Z1 ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[symdiff]) ).

thf(c_0_9,negated_conjecture,
    ! [X29: $i,X30: $i > $o,X31: $i,X32: $i,X33: $i > $o,X34: $i,X35: $i,X36: $i,X37: $i] :
      ( ( ~ ( in @ X31 @ ( dsetconstr @ X29 @ X30 ) )
        | ( in @ X31 @ X29 ) )
      & ( ~ ( in @ X34 @ ( dsetconstr @ X32 @ X33 ) )
        | ( X33 @ X34 ) )
      & ( ~ ( in @ X37 @ ( binunion @ X35 @ X36 ) )
        | ( in @ X37 @ X35 )
        | ( in @ X37 @ X36 ) )
      & ( in @ esk3_0 @ ( symdiff @ esk1_0 @ esk2_0 ) )
      & ( ~ ( in @ esk3_0 @ esk1_0 )
        | ( in @ esk3_0 @ esk2_0 )
        | epred1_0 )
      & ( ( in @ esk3_0 @ esk1_0 )
        | ~ ( in @ esk3_0 @ esk2_0 )
        | epred1_0 )
      & ~ epred1_0 ),
    inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])])])]) ).

thf(c_0_10,plain,
    ( symdiff
    = ( ^ [Z0: $i,Z1: $i] :
          ( dsetconstr @ ( binunion @ Z0 @ Z1 )
          @ ^ [Z2: $i] :
              ( ~ ( in @ Z2 @ Z0 )
              | ~ ( in @ Z2 @ Z1 ) ) ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

thf(c_0_11,negated_conjecture,
    ! [X1: $i,X3: $i,X2: $i > $o] :
      ( ( in @ X1 @ X3 )
      | ~ ( in @ X1 @ ( dsetconstr @ X3 @ X2 ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

thf(c_0_12,plain,
    ! [X1: $i,X3: $i] :
      ( ( dsetconstr @ ( binunion @ X1 @ X3 )
        @ ^ [Z0: $i] :
            ( ~ ( in @ Z0 @ X1 )
            | ~ ( in @ Z0 @ X3 ) ) )
      = ( symdiff @ X1 @ X3 ) ),
    inference(arg_cong,[status(thm)],[c_0_10]) ).

thf(c_0_13,negated_conjecture,
    ! [X1: $i,X3: $i,X2: $i > $o] :
      ( ( X2 @ X1 )
      | ~ ( in @ X1 @ ( dsetconstr @ X3 @ X2 ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

thf(c_0_14,negated_conjecture,
    ! [X1: $i,X3: $i,X4: $i] :
      ( ( in @ X1 @ X3 )
      | ( in @ X1 @ X4 )
      | ~ ( in @ X1 @ ( binunion @ X3 @ X4 ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

thf(c_0_15,negated_conjecture,
    ! [X1: $i,X3: $i,X4: $i] :
      ( ( in @ X1 @ ( binunion @ X3 @ X4 ) )
      | ~ ( in @ X1 @ ( symdiff @ X3 @ X4 ) ) ),
    inference(spm,[status(thm)],[c_0_11,c_0_12]) ).

thf(c_0_16,negated_conjecture,
    ( ( in @ esk3_0 @ esk1_0 )
    | epred1_0
    | ~ ( in @ esk3_0 @ esk2_0 ) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

thf(c_0_17,negated_conjecture,
    ~ epred1_0,
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

thf(c_0_18,negated_conjecture,
    ! [X1: $i,X3: $i,X4: $i] :
      ( ~ ( in @ X1 @ X3 )
      | ~ ( in @ X1 @ X4 )
      | ~ ( in @ X1 @ ( symdiff @ X3 @ X4 ) ) ),
    inference(spm,[status(thm)],[c_0_13,c_0_12]) ).

thf(c_0_19,negated_conjecture,
    ! [X1: $i,X3: $i,X4: $i] :
      ( ( in @ X1 @ X3 )
      | ( in @ X1 @ X4 )
      | ~ ( in @ X1 @ ( symdiff @ X3 @ X4 ) ) ),
    inference(spm,[status(thm)],[c_0_14,c_0_15]) ).

thf(c_0_20,negated_conjecture,
    in @ esk3_0 @ ( symdiff @ esk1_0 @ esk2_0 ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

thf(c_0_21,negated_conjecture,
    ( ( in @ esk3_0 @ esk1_0 )
    | ~ ( in @ esk3_0 @ esk2_0 ) ),
    inference(sr,[status(thm)],[c_0_16,c_0_17]) ).

thf(c_0_22,negated_conjecture,
    ( ( in @ esk3_0 @ esk2_0 )
    | epred1_0
    | ~ ( in @ esk3_0 @ esk1_0 ) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

thf(c_0_23,negated_conjecture,
    ! [X1: $i,X3: $i,X4: $i] :
      ( ~ ( in @ X1 @ ( symdiff @ X3 @ X4 ) )
      | ~ ( in @ X1 @ X3 )
      | ~ ( in @ X1 @ X4 ) ),
    inference(dynamic_cnf,[status(thm)],[c_0_18]) ).

thf(c_0_24,negated_conjecture,
    in @ esk3_0 @ esk1_0,
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21]) ).

thf(c_0_25,negated_conjecture,
    ( ( in @ esk3_0 @ esk2_0 )
    | ~ ( in @ esk3_0 @ esk1_0 ) ),
    inference(sr,[status(thm)],[c_0_22,c_0_17]) ).

thf(c_0_26,negated_conjecture,
    ~ ( in @ esk3_0 @ esk2_0 ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_20]),c_0_24])]) ).

thf(c_0_27,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_25,c_0_24])]),c_0_26]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : SEU611^2 : TPTP v8.2.0. Released v3.7.0.
% 0.13/0.13  % Command    : run_E %s %d THM
% 0.14/0.35  % Computer : n004.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Sun May 19 16:16:23 EDT 2024
% 0.14/0.35  % CPUTime    : 
% 0.20/0.48  Running higher-order theorem proving
% 0.20/0.48  Running: /export/starexec/sandbox/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.50  # Version: 3.1.0-ho
% 0.20/0.50  # Preprocessing class: HSSSSLSSSLMNSFA.
% 0.20/0.50  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.50  # Starting new_ho_10 with 1500s (5) cores
% 0.20/0.50  # Starting full_lambda_3 with 300s (1) cores
% 0.20/0.50  # Starting ho_unfolding_6 with 300s (1) cores
% 0.20/0.50  # Starting sh4l with 300s (1) cores
% 0.20/0.50  # full_lambda_3 with pid 28128 completed with status 0
% 0.20/0.50  # Result found by full_lambda_3
% 0.20/0.50  # Preprocessing class: HSSSSLSSSLMNSFA.
% 0.20/0.50  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.50  # Starting new_ho_10 with 1500s (5) cores
% 0.20/0.50  # Starting full_lambda_3 with 300s (1) cores
% 0.20/0.50  # SinE strategy is GSinE(CountTerms,hypos,1.5,,2,20000,1.0)
% 0.20/0.50  # Search class: HGUSF-FFSF22-DSFFMSBN
% 0.20/0.50  # partial match(2): HGHSF-FFSF22-SSFFMSBN
% 0.20/0.50  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.20/0.50  # Starting new_ho_10 with 163s (1) cores
% 0.20/0.50  # new_ho_10 with pid 28131 completed with status 0
% 0.20/0.50  # Result found by new_ho_10
% 0.20/0.50  # Preprocessing class: HSSSSLSSSLMNSFA.
% 0.20/0.50  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.50  # Starting new_ho_10 with 1500s (5) cores
% 0.20/0.50  # Starting full_lambda_3 with 300s (1) cores
% 0.20/0.50  # SinE strategy is GSinE(CountTerms,hypos,1.5,,2,20000,1.0)
% 0.20/0.50  # Search class: HGUSF-FFSF22-DSFFMSBN
% 0.20/0.50  # partial match(2): HGHSF-FFSF22-SSFFMSBN
% 0.20/0.50  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.20/0.50  # Starting new_ho_10 with 163s (1) cores
% 0.20/0.50  # Preprocessing time       : 0.001 s
% 0.20/0.50  # Presaturation interreduction done
% 0.20/0.50  
% 0.20/0.50  # Proof found!
% 0.20/0.50  # SZS status Theorem
% 0.20/0.50  # SZS output start CNFRefutation
% See solution above
% 0.20/0.50  # Parsed axioms                        : 12
% 0.20/0.50  # Removed by relevancy pruning/SinE    : 7
% 0.20/0.50  # Initial clauses                      : 8
% 0.20/0.50  # Removed in clause preprocessing      : 0
% 0.20/0.50  # Initial clauses in saturation        : 8
% 0.20/0.50  # Processed clauses                    : 25
% 0.20/0.50  # ...of these trivial                  : 0
% 0.20/0.50  # ...subsumed                          : 0
% 0.20/0.50  # ...remaining for further processing  : 24
% 0.20/0.50  # Other redundant clauses eliminated   : 0
% 0.20/0.50  # Clauses deleted for lack of memory   : 0
% 0.20/0.50  # Backward-subsumed                    : 0
% 0.20/0.50  # Backward-rewritten                   : 2
% 0.20/0.50  # Generated clauses                    : 10
% 0.20/0.50  # ...of the previous two non-redundant : 9
% 0.20/0.50  # ...aggressively subsumed             : 0
% 0.20/0.50  # Contextual simplify-reflections      : 1
% 0.20/0.50  # Paramodulations                      : 6
% 0.20/0.50  # Factorizations                       : 0
% 0.20/0.50  # NegExts                              : 0
% 0.20/0.50  # Equation resolutions                 : 0
% 0.20/0.50  # Disequality decompositions           : 0
% 0.20/0.50  # Total rewrite steps                  : 4
% 0.20/0.50  # ...of those cached                   : 2
% 0.20/0.50  # Propositional unsat checks           : 0
% 0.20/0.50  #    Propositional check models        : 0
% 0.20/0.50  #    Propositional check unsatisfiable : 0
% 0.20/0.50  #    Propositional clauses             : 0
% 0.20/0.50  #    Propositional clauses after purity: 0
% 0.20/0.50  #    Propositional unsat core size     : 0
% 0.20/0.50  #    Propositional preprocessing time  : 0.000
% 0.20/0.50  #    Propositional encoding time       : 0.000
% 0.20/0.50  #    Propositional solver time         : 0.000
% 0.20/0.50  #    Success case prop preproc time    : 0.000
% 0.20/0.50  #    Success case prop encoding time   : 0.000
% 0.20/0.50  #    Success case prop solver time     : 0.000
% 0.20/0.50  # Current number of processed clauses  : 13
% 0.20/0.50  #    Positive orientable unit clauses  : 5
% 0.20/0.50  #    Positive unorientable unit clauses: 0
% 0.20/0.50  #    Negative unit clauses             : 2
% 0.20/0.50  #    Non-unit-clauses                  : 6
% 0.20/0.50  # Current number of unprocessed clauses: 0
% 0.20/0.50  # ...number of literals in the above   : 0
% 0.20/0.50  # Current number of archived formulas  : 0
% 0.20/0.50  # Current number of archived clauses   : 11
% 0.20/0.50  # Clause-clause subsumption calls (NU) : 10
% 0.20/0.50  # Rec. Clause-clause subsumption calls : 9
% 0.20/0.50  # Non-unit clause-clause subsumptions  : 1
% 0.20/0.50  # Unit Clause-clause subsumption calls : 1
% 0.20/0.50  # Rewrite failures with RHS unbound    : 0
% 0.20/0.50  # BW rewrite match attempts            : 2
% 0.20/0.50  # BW rewrite match successes           : 1
% 0.20/0.50  # Condensation attempts                : 25
% 0.20/0.50  # Condensation successes               : 0
% 0.20/0.50  # Termbank termtop insertions          : 1458
% 0.20/0.50  # Search garbage collected termcells   : 378
% 0.20/0.50  
% 0.20/0.50  # -------------------------------------------------
% 0.20/0.50  # User time                : 0.005 s
% 0.20/0.50  # System time              : 0.002 s
% 0.20/0.50  # Total time               : 0.007 s
% 0.20/0.50  # Maximum resident set size: 1900 pages
% 0.20/0.50  
% 0.20/0.50  # -------------------------------------------------
% 0.20/0.50  # User time                : 0.005 s
% 0.20/0.50  # System time              : 0.005 s
% 0.20/0.50  # Total time               : 0.011 s
% 0.20/0.50  # Maximum resident set size: 1708 pages
% 0.20/0.50  % E---3.1 exiting
% 0.20/0.50  % E exiting
%------------------------------------------------------------------------------